Chapter 13 Foreign exchange risk Solutions for end-of-chapter questions Questions and problems 1 What are the four FX risks faced by FIs? The four risks include: (i) trading in foreign securities; (ii) making foreign currency loans; (iii) issuing foreign currency-denominated debt; and (iv) buying foreign currency-issued securities. What is the spot market for FX? What is the forward market for FX? What is the position of being net long in a currency? The spot market for foreign exchange involves transactions for immediate delivery of a currency, while the forward market involves agreements to deliver a currency at a later time for a price or exchange rate that is determined at the time the agreement is reached. The net exposure of a foreign currency is the net foreign asset position plus the net foreign currency position. Net long in a currency means that the amount of foreign assets exceeds the amount of foreign liabilities. On 15 December 2011, you convert $500 000 Australian dollars to Japanese yen in the spot foreign exchange market and purchase a one-month forward contract to convert yen into dollars. How much will you receive in US dollars at the end of the month? Use the data in Table 13.1 for this problem. At the beginning of the month you convert $500 000 to yen at a rate of 94.35 yen per dollar, or you will have 500 000 × 94.35 = ¥47 175 000. The one-month forward rate for the US dollar for Japanese yen on 15 July 2009 was 0.010603. So at the end of the month you will convert –¥47 175 000 to dollars at $0.010603 per ¥ or you will have ¥47 175 000 × 0.010603 = $500 196.525. X-IM Bank has SF14 million in assets and SF23 million in liabilities and has sold SF8 million in foreign currency trading. What is the net exposure for X-IM? For what type of exchange rate movement does this exposure put the bank at risk? The net exposure would be SF14 million – SF23 million – SF8 million = –SF17 million. This negative exposure puts the bank at risk of an appreciation of the euro against the dollar. A stronger euro means that repayment of the net position would require more dollars. What two factors directly affect the profitability of an FI’s position in a foreign currency? The profitability is a function of the size of the net exposure and the volatility of the foreign exchange ratio or relationship. The following are the foreign currency positions of an FI, expressed in dollars. Currency Assets Liabilities FX bought FX sold Euro (EUR) $125 000 $50 000 $10 000 $15 000 British pound (GBP) 50 000 22 000 15 000 20 000 Japanese yen (JPY) 75 000 30 000 12 000 88 000 (a) What is the FI’s net exposure in euros? Net exposure in euros = (Assets + FX Bought) – (Liabilities + FX Sold) = $70 000. (b) What is the FI’s net exposure in UK pounds? Net exposure in British pounds = $23 000. (c) What is the FI’s net exposure in Japanese yen? Net exposure in Japanese yen = –$31 000. (d) What is the expected loss or gain if the € exchange rate appreciates by 1 per cent? If assets are greater than liabilities, an appreciation of the foreign exchange rates will generate a gain = $70 000 × 0.01 = $7000. (e) What is the expected loss or gain if the £ exchange rate appreciates by 1 per cent? Gain = $23 000 × 0.01 = $230. (f) What is the expected loss or gain if the € exchange rate appreciates by 2 per cent? Loss = –$31 000 × 0.02 = –$6200. What are the four FX trading activities undertaken by FIs? How do FIs profit from these activities? What are the reasons for the slow growth in FX profits at major banks? The four areas of FX activity undertaken by FIs are either for their customers’ accounts or for their own proprietary trading accounts. They involve the purchase and sale of FX in order to (i) complete international commercial transactions; (ii) invest abroad in direct or portfolio investments; (iii) hedge outstanding currency exposures; and (iv) speculate against movements in currencies. Most banks earn commissions on transactions made on behalf of their customers. If the banks are market makers in currencies, they make their profits on the bid–ask spread. A major reason for the slow growth in profits has been the decline in volatility of FX rates among major European currencies that has more than offset the increased volatility of FX rates among Asian currencies. The reduced volatility is related to the reduction in inflation rates in the European countries and the relatively fixed exchange rates that have prevailed as the European countries move towards full monetary union. City Bank issued $200 million of one-year CDs in the US at a rate of 6.50 per cent. It invested part of this money, $100 million, in the purchase of a one-year bond issued by an Australian firm at an annual rate of 7 per cent. The remaining $100 million was invested in a one-year Brazilian government bond paying an annual interest rate of 8 per cent. The exchange rate at the time of the transaction was Brazilian real (BRL) 1/$1. (a) What will be the net return on this $200 million investment in bonds if the exchange rate between the Brazilian real and the Australian dollar remains the same? Cost of funds = 0.065 × $200 million = $13 million Return on Australian loan = 0.07 × $100 million = $ 7 000 000 Return on Brazilian bond = (0.08 × BRL 100 m)/1.00 = $ 8 000 000 Total interest earned = $15 000 000 Net return on investment = $15 million – $13 million/$200 million = 1.00 per cent. (b) What will be the net return on this $200 million investment if the exchange rate changes to BRL 1.20/$1? Cost of funds = 0.065 × $200 million = $13 000 000 Return on Australian loan = 0.07 × $100 million = $ 7 000 000 Return on Brazilian bond = (0.08 × BRL 100m)/1.20 = $ 6 666 667 Total interest earned = $13 666 667 Net return on investment = $13 666 667 – $13 000 000/$200 000 000 = 0.67 per cent. Consideration should be given to the fact that the Brazilian bond was for BRL 100 million. Thus, at maturity the bond will be paid back for BRL 100 million/1.20 = $83 333 333.33. Therefore, the strengthening dollar will have caused a loss in capital ($16 666 666.67) that far exceeds the interest earned on the Brazilian bond. (c) What will be the net return on this $200 million investment if the exchange rate changes to BRL 0.80/$1? Cost of funds = 0.065 × $200 million = $13 000 000 Return on Australian loan = 0.07 × $100 million = $ 7 000 000 Return on Brazilian bond = (0.08 × Real 100m)/0.80 = $10 000 000 Total interest earned = $17 000 000 Net return on investment = $17 000 000 – $13 000 000/$200 000 000 = 2.00 per cent. Consideration should be given to the fact that the Brazilian bond was for BRL 100 million. Thus, at maturity the bond will be paid back for BRL 100 million/0.80 = $125 000 000. Therefore, the strengthening real will have caused a gain in capital of $25 000 000 in addition to the interest earned on the Brazilian bond. 9 Sun Bank of Byron Bay purchased a 16 million euro one-year loan that pays 12 per cent interest annually. The spot rate for euro is €1.60/$1. Sun Bank has funded this loan by accepting a UK pound-(GBP) denominated deposit for the equivalent amount and maturity at an annual rate of 10 per cent. The current spot rate of the UK pound is $1.60/£1. (a) What is the net interest income earned in dollars on this one-year transaction if the spot rates at the end of the year are €1.70/$1 and $1.85/£1? Loan amount = €16 million/1.60 = $10 million Deposit amount = $10m/1.60 = £6 250 000 Interest income at the end of the year = €16m × 0.12 = €1.92/1.70 = $1 129 411.77 Interest expense at the end of the year = £6 250 000 × 0.10 = £625 000 × 1.85 = $1 156 250 Net interest income = $1 129 411.77 – $1 156 250.00 = –$26 838.23 (b) What should be the GBP to AUD spot rate in order for the bank to earn a net interest margin of 4 per cent? A net interest margin of 4 per cent would imply $10 000 000 × 0.04 = $400 000. The net cost of deposits should be $1 129 411.77 – 400 000 = $729 411.77. Pound rate = $729 411.77/625 000 = $1.1671/£. Thus, the pound should be selling at $1.1671/£ in order for the bank to earn 4 per cent. (c) Does your answer to part (b) imply that the dollar should appreciate or depreciate against the pound? The dollar should appreciate against the pound. It takes fewer dollars to buy one pound. 10 Highlanders Bank recently made a one-year NZD$10 million loan that pays 10 per cent interest annually. The loan was funded with a euro-denominated one-year deposit at an annual rate of 8 per cent. The current spot rate is €1.60/$1. (a) What will be the net interest income in dollars on the one-year loan if the spot rate at the end of the year is €1.58/$1? Interest income and loan principal at year-end = $10m × 0.10 = $1 000 000. Interest expense and deposit principal at year-end = (SF16 000 000 × 0.08)/1.58 = SF1 280 000/1.58 = $810 126.58. Net interest income = $1 000 000 – $810 810.58 = $189 873.42. (b) What will be the net interest return on assets? Net interest return on assets = $189 873.42/$10 000 000 = 0.0190 or 1.90 per cent. (c) How far can the euro appreciate before the transaction will result in a loss for Highlanders Bank? Exchange rate = SF1 280 000/$1 000 000 = SF1.28/$, appreciation of 20.00 per cent. 11 What motivates FIs to hedge foreign currency exposures? What are the limitations to hedging foreign currency exposures? FIs hedge to manage their exposure to currency risks, not to eliminate it. As in the case of interest rate risk exposure, it is not necessarily an optimal strategy to completely hedge away all currency risk exposure. By its very definition, hedging reduces the FI’s risk by reducing the volatility of possible future returns. This narrowing of the probability distribution of returns reduces possible losses, but also reduces possible gains (i.e. it shortens both tails of the distribution). A hedge would be undesirable therefore if the FI wants to take a speculative position in a currency in order to benefit from some information about future currency rate movements. The hedge would reduce possible gains from the speculative position. 12 What are the two primary methods of hedging FX risk for an FI? What two conditions are necessary to achieve a perfect hedge through on-balance-sheet hedging? What are the advantages and disadvantages of off-balance-sheet hedging in comparison to on-balance-sheet hedging? The manager of an FI can hedge using on-balance-sheet techniques or off-balance-sheet techniques. On-balance-sheet hedging requires matching currency positions and durations of assets and liabilities. If the duration of foreign-currency-denominated fixed-rate assets is greater than similar currency denominated fixed-rate liabilities, the market value of the assets could decline more than the liabilities when market rates rise and therefore the hedge will not be perfect. Thus, in matching foreign currency assets and liabilities, not only do they have to be of the same currency but also of the same duration in order to have a perfect hedge. Advantages of off-balance-sheet FX hedging: The use of off-balance-sheet hedging devices, such as forward contracts, enables an FI to reduce or eliminate its FX risk exposure without forfeiting potentially lucrative transactions. On-balance-sheet transactions result in immediate cash flows, whereas off balance-sheet transactions result in contingent future cash flows. Therefore, the upfront cost of hedging using off-balance-sheet instruments is lower than the cost of on-balance-sheet transactions. Moreover, since on-balance-sheet transactions are fully reflected in financial statements, there may be additional disclosure costs to hedging on the balance sheet. Off-balance-sheet hedging instruments have been developed for many types of risk exposures. For currency risk, forward contracts are available for the majority of currencies at a variety of delivery dates. Moreover, since the forward contract is negotiated over the counter, the counterparties have maximum flexibility to set terms and conditions. Disadvantages of off-balance-sheet FX hedging: There is some credit risk associated with off-balance-sheet hedging instruments since there is some possibility that the counterparty will default on its obligations. This credit risk exposure is exacerbated in negotiated markets such as the forward market, but mitigated for exchange-traded hedging instruments such as futures contracts. 13 Brumby Bank has been borrowing in the Australian markets and lending abroad, thus incurring foreign exchange risk. In a recent transaction, it issued $2 million in one-year securities at 6 per cent and funded a loan in euro at 8 per cent. The spot rate for the euro was €1.45/$1 at the time of the transaction. (a) Information received immediately after the transaction closing indicated that the euro will depreciate to €1.47/$1 by year-end. If the information is correct, what will be the realised spread on the loan? What should have been the bank interest rate on the loan to maintain the 2 per cent spread? Assume adjustments in principal value are included in the spread. Amount of loan in € = $2 million × 1.45 = €2.9 million. Interest and principal at year-end = €2.9m × 1.08 = €3.132m/1.47 = $2 130 612.24 Interest and principal of CDs = $2m × 1.06 = $2 120 000 Net interest income = $2 130 612.24 – $2 120 000 = $10 612.24 Net interest margin = $10 612.24/2 000 000 = 0.0053 or 0.53 per cent. In order to maintain a 2 per cent spread, the interest and principal earned at €1.47/$ should be: €2.9 (1 + x)/1.47 = 2.16 (because 2.16 – 2.12/2.00 = 0.02). Therefore, (1 + x) = (2.16 × 1.47)/ €2.9 = 1.0949, and x = 0.0949 or 9.49 per cent. (b) The bank had an opportunity to sell one-year forward euros at €1.46/$1. What would have been the spread on the loan if the bank had hedged forward its foreign exchange exposure? Net interest income if hedged = €2.9 × 1.08 = 3.132/1.46 = 2.1452m – 2.12m = 0.0252 million, or $25 205.48 Net interest margin = 0.0252/2 = 0.0126, or 1.26 per cent (c) What would have been an appropriate change in loan rates to maintain the 2 per cent spread if the bank intended to hedge its exposure using the forward contract rates? To maintain a 2 per cent spread: €2.9(1 + X)/1.46 = 2.16 => X = 8.74 per cent. The bank should increase the rates to 8.74 per cent and hedge with the sale of forward €s to maintain a 2 per cent spread. 14 A bank purchases a six-month, $1 million Eurodollar deposit at an annual interest rate of 6.5 per cent. It invests the funds in a six-month Swedish krona bond paying 7.5 per cent per year. The current spot rate is $0.18/SEK1. (a) The six-month forward rate on the Swedish krona is being quoted at $0.1810/SEK1. What is the net spread earned on this investment if the bank covers its foreign exchange exposure using the forward market? Interest plus principal expense on six-month CD = $1m × (1 + 0.065/2) = $1 032 500 Principal of Swedish bond = $1 000 000/0.18 = SEK555 555.56 Interest and principal = SEK5 555 555.56 × (1 + 0.075/2) = SEK5 763 888.89 Interest and principal in dollars if hedged: SEK5 763 888.89 × 0.1810 = $1 043 263.89 Spread = $1 043 263.89–1 032 500 = $10 763.89/1 million = 0.010764, or 2.15 per cent p.a. (b) What forward rate will cause the spread to be only 1 per cent per year? Net interest income should be = 0.005 × 1 000 000 = $5000 Therefore, interest income should be = $1 032 500 + $5000 = $1 037 500 Forward rate = SEK5 763 888.89/$1 037 500 = $0.18/SK For the spread to remain at 1 per cent the spot and the forward will have to be the same. (c) Explain how forward and spot rates will both change in response to the increased spread. If FIs are able to earn higher spreads in other countries and guarantee these returns by using the forward markets, these are equivalent to risk-free investments (except for default risk). As a result, in part (a) there will be an increase in demand for the Swedish krona in the spot market and an increase in sale of the forward SEK as more banks engage in this kind of lending. This results in an appreciation of the spot SEK and a depreciation of the forward SEK until the spread is zero for securities of equal risk. (d) Why will a bank still be able to earn a spread of 1 per cent knowing that interest rate parity usually eliminates arbitrage opportunities created by differential rates? In part (b), the FI is still able to earn a spread of 1 per cent because the risk of the securities is not equal. The FI earns an extra 1 per cent because it is lending to an AA-rated firm. The dollar-denominated deposits in the euro currency markets are rated higher because these deposits usually are issued by large institutions. Thus, the 1 per cent spread reflects credit or default risk. If the FI were to invest in securities of equal risk in Sweden, arbitrage would ensure that the spread is zero. 15 How does the lack of perfect correlation of economic returns between international financial markets affect the risk–return opportunities for FIs holding multicurrency assets and liabilities? Refer to Table 13.6. Which country pairings seem to have the highest correlation of equity and bond returns? If financial markets are not perfectly correlated, they provide opportunities to diversify and reduce risk from mismatches in assets and liabilities in individual currencies. The benefits of diversification depend on the extent of the correlations. The lower the correlation, the greater the benefits. However, FIs that only hold one or two foreign assets and liabilities cannot take advantage of these benefits and have to hedge their individual portfolio exposures. From Table 13.6, in order of rank the country pairs with the highest correlations are Canada–United States, Germany–United Kingdom, United Kingdom–United States, United Kingdom–Canada, Germany–United States, and Germany–Canada. The correlations are much lower in the bond markets. In order of rank the country pairs with the lowest correlations are Germany–Canada, United Kingdom–Canada, Germany–United States, United Kingdom–United States, Canada–United States, and Germany–United Kingdom. 16 What is the purchasing power parity theorem? As relative inflation rates (and interest rates) change, foreign currency exchange rates that are not constrained by government regulation should also adjust to account for relative differences in the price levels (inflation rates) between the two countries. According to purchasing power parity (PPP), foreign currency exchange rates between two countries adjust to reflect changes in each country’s price levels (or inflation rates and implicitly interest rates) as consumers and importers switch their demands for goods from relatively high inflation (interest) rate countries to low inflation (interest) rate countries. Specifically, the PPP theorem states that the change in the exchange rate between two countries’ currencies is proportional to the difference in the inflation rates in the two countries. 17 Suppose that the current spot exchange rate of US dollars for Australian dollars, SUS$/A$, is .7590 (i.e. 0.759 dollars, or 75.9 cents, can be received for A$1). The price of Australian-produced goods increases by 5 per cent (i.e. inflation in Australia, IPA, is 5 per cent), and the US price index increases by 3 per cent (i.e. inflation in the United States, IPUS, is 3 per cent). Calculate the new spot exchange rate of US dollars for Australian dollars that should result from the differences in inflation rates. According to PPP, the 5 per cent rise in the price of Australian goods relative to the 3 per cent rise in the price of US goods results in a depreciation of the Australian dollar (by 2 per cent). Specifically, the exchange rate of Australian dollars to US dollars should fall, so that: iUS – iA = ΔSUS$/A$/SUS$/A$ Plugging in the inflation and exchange rates, we get: 0.03 – 0.05 = ΔSUS$/A$/SUS$/A$ = ΔSUS$/A$/ 0.759 or: 0–.02 = ΔSUS$/A$/0.759 and: ΔSUS$/A$ = –(0.02) × 0.759 = –0.01518 Thus, it costs 1.518 cents less to receive an Australian dollar (or it costs 15.98 cents (75.9 cents – 1.518 cents), or 0.74382 of $1, can be received for 1 Australian dollar). The Australian dollar depreciates in value by 2 per cent against the US dollar as a result of its higher inflation rate. 18 Explain the concept of interest rate parity. What does this concept imply about the long-run profit opportunities from investing in international markets? What market conditions must prevail for the concept to be valid? Interest rate parity argues that the discounted spread between domestic and foreign interest rates is equal to the percentage spread between forward and spot exchange rates. If interest rate parity holds, then it is not possible for FIs that borrow and lend in different currencies to take advantage of the differences in interest rates between countries. This is because the spot and forward rates will adjust to ensure that no arbitrage can take place through cross-border investments. If a disparity exists, the sale and purchase of spot and forward currencies by arbitragers will ensure that in equilibrium interest rate parity is maintained. 19 Assume that annual interest rates are 8 per cent in Australia and 4 per cent in Germany. An FI can borrow (by issuing one-year securities) or lend (by purchasing one-year securities) at these rates. The spot rate is $0.60/€1. If the forward rate is $0.64/€1, how could the FI arbitrage using a sum of $1 million? What is the expected spread? Borrow $1 000 000 in Australia by issuing one-year securities Interest and principal at year-end = $1 000 000 × 1.08 = $1 080 000 Make a loan in Germany Interest and principal = $1 000 000/0.60 = €1 666.667 × 1.04 = €1 733 333 Purchase AUD at the forward rate of $0.64 × 1 733 333 = $1 109 333.33 Spread = $1 109 333.33 – $1 080 000 = $29 333.33/1 000 000 = 2.93% (b) What forward rate will prevent an arbitrage opportunity? The forward rate that will prevent any arbitrage is given by solving the following equation: Ft = [(1 + 0.08) × 0.60]/(1.04) = $0.6231/€ 20 How does the lack of perfect correlation of economic returns between international financial markets affect the risk–return opportunities for FIs holding multicurrency assets and liabilities? If financial markets are not perfectly correlated, they provide opportunities to diversify and reduce risk from mismatches in assets and liabilities in individual currencies. The benefits of diversification depend on the extent of the correlations. The smaller the correlation, the greater the benefits. However, FIs that only hold one or two foreign assets and liabilities cannot take advantage of these benefits and have to hedge their individual portfolio exposures. 21 What is the relationship between the real interest rate, the expected inflation rate and the nominal interest rate on fixed-income securities in any particular country? Refer to Table 13.6. What factors may be the reasons for the relatively high correlation coefficients? The nominal interest rate is equal to the real interest rate plus the expected inflation rate on assets where default risk is not an issue. The strength of correlations among countries whose economies are considered to be the leaders of the industrialised nations is evidence that the world capital markets among these markets are reasonably well integrated. 22 What is economic integration? What impact does the extent of economic integration of international markets have on the investment opportunities for FIs? If markets are not perfectly correlated, some barriers to free trade exist between the markets and therefore they are not fully integrated. When markets are fully integrated, opportunities for diversification are reduced. Also, real returns across countries are equal. Thus, diversification benefits occur only when nominal and real rates differ between countries. This happens when some formal or informal barriers exist to prevent the free flow of capital across countries. 23 An FI has $100 000 of net positions outstanding in UK pounds (£) and –$30 000 in Swiss francs (CHF). The standard deviation of the net positions as a result of exchange rate changes is 1 per cent for the £ and 1.3 per cent for the CHF. The correlation coefficient between the changes in exchange rates of the £ and the CHF is 0.80. (a) What is the risk exposure to the FI of fluctuations in the £/$ rate? Since the FI has a positive £ position, an appreciation of the £ will increase the value of its £–denominated assets more than its liabilities, providing a net gain. The opposite will occur if the £ depreciates. (b) What is the risk exposure to the FI of fluctuations in the CHF/$ rate? Since the FI has a negative net position in Swiss francs, the value of its Swiss-denominated assets will increase in value but not as greatly as the value of its liabilities. Hence, an appreciation of the CHF will lead to a net loss. The opposite will occur if the currency depreciates. (c) What is the risk exposure if both the £ and the CHF positions are combined? Use the formula: = $72 671 The FI’s net position is actually $72 671. Without including correlation, the exposure is estimated at $100 000 – $30 000 = $70 000. 24 A US money market mutual fund manager is looking for some profitable investment opportunities and observes the following one-year interest rates on government securities and exchange rates: rUS = 12 per cent, rUK = 9 per cent, S = $1.50/£1, f = $1.6/£1, where S is the spot exchange rate and f is the forward exchange rate. Which of the two types of government securities would constitute a better investment? The UK securities would yield a higher return. Compared with the 12 per cent return in the US, a US investor could convert $1 000 000 to £666 667 and invest it at 9 per cent. In one year the expected return of principal and interest is £726 667. If these pounds are sold forward at $1.6/£1, the investor will lock in $1 162 667 for a 16.2 per cent return. 25 What factors may make the use of swaps or forward contracts preferable to the use of futures contracts for the purpose of hedging long-term foreign exchange positions? A primary factor is that futures contracts may not be available on the day the hedge is desired, or the desired maturity may not be available. If the maturity of the available contract is less than the desired hedge maturity, the FI will incur additional transaction costs from rolling the futures contract to meet the desired hedge maturity. Such action incurs additional uncertainty about the price of the contracts in the future. 26 An FI has an asset investment in euros. The FI expects the exchange rate of $/€ to increase by the maturity of the asset. (a) Is the dollar appreciating or depreciating against the euro? The dollar is depreciating as it will take more dollars per euro in the future. (b) To fully hedge the investment, should the FI buy or sell euro futures contracts? The FI should buy euro futures. (c) If there is perfect correlation between changes in the spot and futures contracts, how should the FI determine the number of contracts necessary to hedge the investment fully? A sufficient number of futures contracts should be purchased so that a loss (profit) on the futures position will just offset a profit (loss) on the cash loan portfolio. If there is perfect correlation between the spot and futures prices, the number of futures contracts can be determined by dividing the value of the foreign currency asset portfolio by the foreign currency size of each contract. If the spot and futures prices are not perfectly correlated, the value of the long asset position at maturity must be adjusted by the hedge ratio before dividing by the size of the futures contract. 27 What is meant by ‘tailing the hedge’? What factors allow an FI manager to tail the hedge effectively? Gains from futures contract positions typically are received throughout the life of the hedge from the process of marking to market the futures position. These gains can be reinvested to generate interest income cash flows that reduce the number of futures contracts needed to hedge an original cash position. Higher short-term interest rates and less uncertainty in the pattern of expected cash flows from marking to market the futures position will increase the effectiveness of this process. 28 What does the hedge ratio measure? Under what conditions is this ratio valuable in determining the number of futures contracts necessary to hedge fully an investment in another currency? How is the hedge ratio related to basis risk? The hedge ratio measures the relative sensitivity of futures prices to changes in the spot exchange rates. This ratio is particularly helpful when the changes in futures prices are not perfectly correlated with the changes in the spot exchange rates. The hedge ratio is a measure of the basis risk between the futures and spot exchange rates. 29 What technique is commonly used to estimate the hedge ratio? What statistical measure is an indicator of the confidence that should be placed in the estimated hedge ratio? What is the interpretation if the estimated hedge ratio is greater than one? Less than one? A common method to estimate the hedge ratio is to regress recent changes in spot prices on recent changes in futures prices. The degree of confidence is measured by the value of R2 for the regression. A value of R2 equal to one implies perfect correlation between the two price variables. The estimated slope coefficient () from the regression equation is the estimated hedge ratio or measure of sensitivity between spot prices and futures prices. A value of greater than one means that changes in spot prices are greater than changes in futures prices, and the number of futures contracts must be increased accordingly. A value of less than one means that changes in spot prices are less than changes in futures prices, and the number of futures contracts can be decreased accordingly. 30 An FI has assets denominated in UK pound sterling of A$125 million and sterling liabilities of A$100 million. (a) What is the FI’s net exposure? The net exposure is $125 million – $100 million = $25 million. (b) Is the FI exposed to an A$ appreciation or depreciation? The FI is exposed to dollar appreciation, or declines in the pound relative to the A$. (c) How can the FI use futures or forward contracts to hedge its FX rate risk? The FI can hedge its FX rate risk by selling forward or futures contracts in pound sterling, assuming the contracts are quoted as A$/£. (d) What is the number of futures contracts to be utilised to hedge fully the FI’s currency risk exposure? Assuming that the contract size for British pounds is £62 500, the FI must sell Nf = A$25 million/£62 500 = 400 pound sterling futures contracts. (e) If the British pound falls from $1.60/£ to $1.50/£, what will be the impact on the FI’s cash position? The cash position will witness a loss if the pound sterling depreciated in terms of the US dollar. The loss would be equal to the net exposure (in A$) multiplied by the FX rate shock ( St) = $5 million ($1.50 – $1.60) = –$2.5 million. (f) If the British pound futures price falls from $1.55/£ to $1.45/£, what will be the impact on the FI’s futures position? The gain on the short futures hedge is: Nf × 62 500 × ft = –400($62 500)($1.45 – $1.55) = +$2.5 million (g) Using the information in parts (e) and (f), what can you conclude about basis risk? In cases where basis risk does not occur, such as in this problem, a perfect hedge is possible. In other words, in this case the hedge ratio = 1.0. 31 An FI is planning to hedge its one-year $100 million Swiss franc (SF)-denominated loan against exchange rate risk. The current spot rate is $0.60/SF. A one-year SF futures contract is currently trading at $0.58/SF. SF futures are sold in standardised units of SF125 000. (a) Should the FI be worried about the SF appreciating or depreciating? The FI should be worried about the SF depreciating because it will provide fewer dollars per SF. (b) Should it buy or sell futures to hedge against exchange rate exposure? The FI should sell SF futures contracts to hedge this exposure. (c) How many futures contracts should it buy or sell if a regression of past spot prices on future prices generates an estimated slope of 1.4? Nf = (Long asset position × br)/(Futures contract size) = $100m × 1.4/SF125 000 = 1120 contracts (d) Show exactly how the FI is hedged if it repatriates its principal of SF100 million at year-end, the spot price of SF at year-end is $0.55/SF, and the forward price is $0.5443/SF. The original loan in dollars = SF100 × $0.60 = $60 million, and the loan value in dollars at year-end = SF100 × $0.55 = $55 million. The balance sheet has decreased in value by $5 000 000. The gain from hedge = ($0.58 – $0.5443) × SF125 000 × 1120 = $4 998 000. 32 An FI has a $100 million portfolio of six-year Eurodollar bonds that have an 8 per cent coupon. The bonds are trading at par and have a duration of five years. The FI wishes to hedge the portfolio with T-bond options that have a delta of –0.625. The underlying long-term Treasury Bonds for the option have a duration of 10.1 years and trade at a market value of $96 157 per $100 000 of par value. Each put option has a premium of $3.25. (a) How many bond put options are necessary to hedge the bond portfolio? (b) If interest rates increase 100 basis points, what is the expected gain or loss on the put option hedge? A $100 000 20-year, 8 per cent bond selling at $96 157 implies a yield of 8.4 per cent. P = p × Np = 824 × –0.625 × –10.1/1.084 × $96 157 × 0.01 = $4 614 028 gain (c) What is the expected change in market value on the bond portfolio? PVBond = –5 × 0.01/1.08 × $100 000 000 = –$4 629 629.63 (d) What is the total cost of placing the hedge? The price quote of $3.25 is per $100 of face value. Therefore, the cost of one put contract is $3250, and the cost of the hedge = 824 contracts × $3250 per contract = $2 678 000. (e) How far must interest rates move before the payoff on the hedge will exactly offset the cost of placing the hedge? Solving for the change in interest rates gives R = ($3250 × 1.084)/(0.625 × 10.1 × $96 157) = 0.005804 or 0.58 per cent. (f) How far must interest rates move before the gain on the bond portfolio will exactly offset the cost of placing the hedge? Again solving for R = ($3250 × 824 × 1.08)/(5 × $100 000 000) = 0.0057844 or 0.58 per cent. (g) Summarise the gain, loss, cost conditions of the hedge on the bond portfolio in terms of changes in interest rates. If rates increase 0.58 per cent, the portfolio will decrease in value approximately equal to the gain on the hedge. This position corresponds to the intersection of the payoff function from the put and the X-axis in Figure7.16 in the textbook. The FI is out the cost of the hedge, which also will be the case for any other increase in interest rates. In effect the cost of the hedge is the insurance premium to assure the yield on the portfolio at the time the hedge is placed. If rates decrease approximately 0.58 per cent, the gain on the portfolio will offset the cost of the hedge, and the put option will not be exercised. Any increase in rates beyond 0.58 per cent will generate positive profits for the portfolio in excess of the cost of the hedge. 33 An FI must make a single payment of 500 000 Swiss francs (SF) in six months at the maturity of a CD. The FI’s in-house analyst expects the spot price of the franc to remain stable at the current $0.80/SF. But the analyst is concerned that it could rise as high as $0.85/SF or fall as low as $0.75/SF. Because of this uncertainty, the analyst recommends that as a precaution the FI hedge the CD payment using either options or futures. Six-month call and put options on the Swiss franc with an exercise price of $0.80/SF are trading at 4 cents and 2 cents, respectively. A six-month futures contract on the Swiss franc is trading at $0.80/SF. (a) Should the analyst be worried about the dollar depreciating or appreciating? The analyst should be worried about the dollar depreciating. (b) If the FI decides to hedge using options, should the FI buy put or call options to hedge the CD payment? Why? The analyst should buy call options on Swiss francs, because if the dollar depreciates to $0.85/SF, the call options will be in the money. (c) If futures are used to hedge, should the FI buy or sell Swiss franc futures to hedge the payment? Why? The FI should buy futures, because if the dollar depreciates to $0.85/Sf, your cash flows will be positive on the futures position. (d) What will be the net payment on the CD if the selected call or put options are used to hedge the payment? Assume the following three scenarios: the spot price in six months will either be $0.75, $0.80 or $0.85/SF. Also assume that the options will be exercised. Using call options, the net payments are: Future spot prices $0.75 $0.80 $0.85 Premium on call options –$ 20 000 –$ 20 000 –$20 000 (0.04 × 500 000) Gain/loss on exercise 0 0 $25 000 Purchase of spot –$375 000 –$400 000 –$425 000 Net payment –$395 000 –$420 000 –$420 000 (e) What will be the net payment if futures had been used to hedge the CD payment? Use the same three scenarios as in part (d). Using futures, the net payments are: Future spot prices $0.75 $0.80 $0.85 Gain/loss on exercise –$25 000 0 $25 000 Purchase of spot –$375 000 –$400 000 –$425 000 Net payment –$400 000 –$400 000 –$400 000 (f) Which method of hedging is preferable after the fact? Ex-post it appears that hedging with futures will result in the lowest payments in dollars, at least until the spot reaches $0.76/SF, at which time both net payments will be similar. If the dollar appreciates beyond $0.76/SF, that is, to $0.74/SF or $0.72/SF, then the option hedges result in lower payments. Once again, this is an ex-post conclusion. Ex-ante, it depends on your projections of the expected future spot rates. 34 An FI has made a loan commitment of SF10 million that is likely to be taken down in six months. The current spot rate is $0.60/SF. (a) Is the FI exposed to the dollar depreciating or the dollar appreciating? Why? The FI is exposed to the dollar depreciating, because it would require more dollars to purchase the SF10 million if the loan is drawn down as expected. (b) If it decides to hedge using SF futures, should it buy or sell SF futures? It should buy SF futures if it decides to hedge against a likely depreciation of the dollar. (c) If the spot rate six months from today is $0.64/SF, what dollar amount is needed in six months if the loan is drawn down? If it had remained unhedged, it would require $0.64 × SF10 000 000 = $6.4 million to make the SF-denominated loan. (d) A six-month SF futures contract is available for $0.61/SF. What is the net amount needed at the end of six months if the FI had hedged using the SF10 million of futures contract? Assume futures prices are equal to spot at the time of payment, that is, at maturity. If it has hedged using futures, it will gain ($0.64 – $0.61) × SF10 million = $300 000 on its futures position. Its net payment will be $6.1 million. (e) If it decides to use options to hedge, should it purchase call or put options? It should purchase call options if it has to hedge against the likely drawdown. (f) Call and put options with an exercise price of $0.61/SF are selling for $0.02 and $0.03, respectively. What is the net amount needed by the FI at the end of six months if it had used options instead of futures to hedge this exposure? Premium on call options = $0.02 × SF10m = $200 000. Purchase at spot = $0.64 × SF10 million = $6.4 million. Gain on options = $0.03 × SF10 million = $300 000. Its net payment will be $6.3 million. Two multinational corporations enter their respective debt markets to issue $100 million of two-year notes. Firm A can borrow at a fixed annual rate of 11 per cent or a floating rate of LIBOR plus 50 basis points, repriced at the end of the year. Firm B can borrow at a fixed annual rate of 10 per cent or a floating rate of LIBOR, repriced at the end of the year. (a) If Firm A is a positive duration gap insurance company and Firm B is a money market mutual fund, in what market(s) should each firm borrow so as to reduce their interest rate risk exposures? Firm A will prefer to borrow in the fixed-rate debt market in order to generate positive cash flows when interest rates increase. This will offset the impact of an increase in interest rates, which would cause the market value of the insurance company’s equity to decline. Firm B will prefer to borrow in the floating-rate debt market so as to better match the duration of its short-term assets. (b) In which debt market does Firm A have a comparative advantage over Firm B? The matrix of possible interest rates is given below. Fixed rate Variable rate Firm A 11.0% L + 0.50% Firm B 10.0% L % Difference 1.0% 0.5% Firm A has a comparative advantage in the floating-rate market and Firm B has a comparative advantage in the fixed-rate market. This is because the default risk premium of Firm A over Firm B is 50 basis points in the floating-rate market and 100 basis points in the fixed-rate market. (c) Although Firm A is riskier than Firm B, and therefore must pay a higher rate in both the fixed-rate and floating-rate markets, there are possible gains to trade. Set up a swap to exploit Firm A’s comparative advantage over Firm B. What are the total gains from the swap trade? Assume a swap intermediary fee of 10 basis points. The total gains to the swap trade are 50 basis points (the price differential on Firm A’s default risk premium over Firm B) less 10 basis points (the swap intermediary fee). Both Firms A and B can exploit this price differential by issuing in the debt market in which they have comparative advantage and then swapping the interest payments. The 40 basis points can be allocated to either Firm A and/or Firm B according to the terms of the swap. A possible set of feasible swap rates that give all of the gains to Firm A (see part (d) below) is illustrated here. Evidence that Firm A receives all of the benefits is given in the payoff matrix below. Firm A Firm B Cash market liability rate L + 0.5% 10.0% Minus Swap-in rate –(L %) –10.0% Plus Swap-out rate + 10.0% +(L %) Net financing cost rate 10.5% L % Less intermediary fee 0.1% Financing cost rate net of fee 10.6% Firm A is paying the intermediary fee, since Firm B is receiving no benefits from this swap transaction. The 40 basis point net differential could be shared in a number of other combinations where Firm A received most (exploited) of the benefit. (d) The gains from the swap trade can be apportioned between Firm A and B through negotiation. What terms of trade would give all the gains to Firm A? What terms of trade would give all the gains to Firm B? All the gains go to Firm A if Firm B pays LIBOR for Firm A’s floating-rate debt. Then Firm A must pay 10 per cent for Firm B’s fixed-rate debt plus 50 basis points on Firm A’s floating-rate debt plus 10 basis points for the swap intermediary’s fee. The total fixed annual interest cost to Firm A is 10.6 per cent, a savings of 40 basis points over the cash market fixed rate of 11 per cent. This swap rate apportionment is illustrated in part (c) above. All the gains go to Firm B if Firm A pays 11 per cent for Firm B’s fixed-rate, 10 per cent debt. Then Firm B pays LIBOR plus 50 basis points on Firm A’s floating-rate debt for a net savings of 50 basis points. The savings occur because Firm B receives an excess 1.0 per cent from Firm A, but must pay 50 basis points more to Firm A than it would pay in the cash floating-rate market. Firm A must pay 11 per cent against Firm B’s fixed-rate debt, but receives its exact liability payment from Firm B. A diagram of this allocation is given below. In this example, Firm B would pay the swap intermediary fee of 10 basis points, and thus would realise a net, after-fee savings of 40 basis points. The payoff matrix is given below. Firm A Firm B Cash market liability rate L + 0.5% 10.0% Minus Swap-in rate –(L + 0.5 %) –11.0% Plus Swap-out rate + 11.0% +(L + 0.5 %) Net financing cost rate 11.0% L–0.5% Less intermediary fee 0.1% Financing cost rate net of fee L–0.4% (e) Assume swap pricing that allocates all the gains from the swap to Firm A. If A buys the swap from B and pays the swap intermediary’s fee, what are the end-of-year net cash flows if LIBOR is 8.25 per cent? Firm A (in millions of dollars) Firm B (in millions of dollars) A pays out fixed rate ($10.00) B pays out LIBOR ($8.25) A receives LIBOR from B $8.25 B receives fixed rate from A $10.00 A pays floating rate to creditors (L + 0.5%) ($8.75) B pays fixed rate to creditors ($10.00) A pays intermediary fee ($0.10) A’s net cash inflow ($10.60) B’s net cash inflow ($8.25) This solution is an extension of the diagram in part (c) and the explanation at the beginning of part (d) above where LIBOR is 8.25 per cent. The summary shows the effective cost rate converted to dollars for the total cash flows of each firm. However, the cash flows in a swap arrangement include only the differential cash flows between the two parties. Thus, at end of year, Firm A would pay $1.75 ($10.00 – $8.25) to Firm B and $0.10 to the intermediary for a total cash flow on the swap arrangement of $1.85. Firm B receives $1.75 from Firm A. (f) If Firm A buys the swap in part (e) from Firm B and pays the swap intermediary’s fee, what are the end-of-year net cash flows if LIBOR is 11 per cent? Be sure to net swap payments against cash market payments for both firms. Firm A (in millions of dollars) Firm B (in millions of dollars) A pays out fixed rate ($10.00) B pays out LIBOR ($11.00) A receives LIBOR from B $11.00 B receives fixed rate from A $10.00 A pays floating rate to creditors (L + 0.5%) ($11.50) B pays fixed rate to creditors ($10.00) A pays intermediary fee ($0.10) A’s net cash inflow ($10.60) B’s net cash inflow ($11.00) Even though LIBOR has increased to 11 per cent, Firm A’s total effective cost rate has not changed. The rate remains at 10.60 per cent, or a total of $10.60 million. However, the cost rate for Firm B has increased because LIBOR has increased. Thus, the actual cash flows in the swap transaction now become that Firm B pays $1.00 ($11 – $10) to Firm A, and that Firm A receives $1.00 and pays out $0.10 to the intermediary. Each firm must, of course, pay the cash market liability rates. (g) If all barriers to entry and pricing inefficiencies between Firm A’s debt markets and Firm B’s debt markets were eliminated, how would that affect the swap transaction? If relative prices are the same in the markets of both Firm A and B, then there are no potential gains to trade and therefore no swap transactions can take place. They will each issue debt in their own markets. Web question 36 Go to the Reserve Bank of Australia’s website and update Tables 13.1 and 13.3. Be prepared to discuss any changes in either the size and/or the maturity structures of the foreign exchange exposures. The answer will depend on the date of the assignment. See the Reserve Bank website at www.rba.gov.au/Statistics/Bulletin/F09hist.xls. Solution Manual for Financial Institutions Management Anthony Saunders, Marcia Cornett, Patricia McGraw 9780070979796, 9780071051590
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